Apparatus and method for measurement of weak optical absorptions by thermally induced laser pulsing

ABSTRACT

The thermal lensing phenomenon is used as the basis for measurement of weak optical absorptions when a cell containing the sample to be investigated is inserted into a normally continuous-wave operation laser-pumped dye laser cavity for which the output coupler is deliberately tilted relative to intracavity circulating laser light, and pulsed laser output ensues, the pulsewidth of which can be related to the sample absorptivity by a simple algorithm or calibration curve. A minimum detection limit of less than 10 -5  cm -1  has been demonstrated using this technique.

This invention is the result of a contract with the Department of Energy(Contract No. W-7405-ENG-36).

BACKGROUND OF THE INVENTION

The present invention relates generally to the measurement of weakoptical absorptions and more particularly to the use of the thermoopticeffect which occurs when a laser beam traverses a weakly absorbingsolution forming a negative thermal lens which lens, when automaticallycorrecting for a deliberate optical misalignment of a laser cavity intowhich the sample under investigation is inserted, causes pulsedoperation in what would normally be continuous laser output, thepulsewidth of this output being related to the sample absorptivity.

When a laser beam traverses a weakly absorbing solution a negativethermal lens is formed in the solution due to heating of the liquid.This is one manifestation of the thermooptic effect, and it can be usedto measure small absorptivities, α, of solutions or molar extinctioncoefficient of solutes, ε_(s) =α_(s) /c, where α_(s) is the absorptivityof the solute and c is the solute concentration in a particular solvent.A cell containing the solution to be studied is inserted into the cavityof a normally continuous-wave dye laser. If the plane of the outputcoupler of the laser is intentionally misaligned slightly, the laserbegins pulsed operation at a frequency essentially independent of α andonly slightly dependent on the extent of the cavity misalignment. Thepulses are equally spaced and have identical pulsewidths which width isstrongly dependent on the absorptivity of the sample solution. Suchpulsewidths may decrease by as much as a factor of 100 as theabsorptivity is increased making this characteristic useful formeasuring weak absorptivities of solutions.

The thermooptic phenomenon has been known for many years, and has beenused for almost as many years for absorption measurements. Reference 1describes transient effects in lasers with liquid samples inserted inthe laser cavity, but the method and apparatus of the instant inventionutilizes a different manifestation of the thermooptic effect from otherprevious absorption measurement techniques or this transient-basedmethod.

1. In "Long-Transient Effects in Lasers with Inserted Liquid Samples,"by J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto and J. R.Whinnery, J. Appl. Phys. 36, 3 (1965), the buildup and decay of theoutput of a helium-neon laser when absorbing liquids were placed withinits resonator cavity is described. The application of the authors'method to measurement of small absorbances is mentioned although notelaborated upon. The transient buildup and decay of the laser outputtakes place over a timescale of several seconds and appears to beexplainable by the simple heating of the liquid with the formation of athermal lens which simply either improves or causes the deterioration ofthe laser cavity alignment, thereby effecting its output. The effectcould not be correctly described as a laser oscillatory or pulsedoperation as occurs in our invention. Further, their system, unlikeours, works better when operated near the threshold of stable laseraction. Moreover, the intentional misalignment of the cavity outputcoupler which gives rise to the approximately 5 Hz oscillation in outputof the instant invention is not taught by this reference. That is, theadvantage of having a repetitive and highly reproducible laser signalwhich can be easily related to the sample absorptivity in that suchsignals are readily treated using standard detection and averagingtechniques to achieve the maximum signal-to-noise ratio and thereforethe greatest measurement sensitivity and range is not deducible from theGordon et al. paper.

2. In "Time-Resolved Thermal Lens Calorimetry," by N. J. Dovichi and J.M. Harris, Anal. Chem. 53, 106 (1981), the authors describe a kineticapproach to measurements involving the thermal lens generation in weaklyabsorbing liquids. Therein it is explained that obtaining quantitativeinformation from the time dependence of the signal derived from pulsingor chopping the heating laser is more efficient and reproducible thansimply measuring the initial and final signal amplitudes alone with along time delay in between these two sampling points. It is also pointedout that the signals obtained are more readily analyzed if one samplesthe output from the sample cell at short times since the thermal lensformed will then be relatively thin. No mention is made of intracavityinsertion of the sample, with consequent oscillation of the laseroutput, however, as is described in the instant invention.

3. A more theoretical discussion of the time-resolved thermoopticphenomenon is found in "Photothermal Deflection Spectroscopy andDetection," by W. B. Jackson, N. M. Amer, A. C. Boccara, and D.Fournier, Appl. Optics 20, 1333 (1981). The authors describe the mostcommon working embodiments of the thermooptic detection technique knownin the art and show them schematically in their FIG. 4. As in Ref. 2, nomention is made of intracavity gain modulation by an absorbing mediumunder investigation.

References 1-3 then, provide no guidance for one skilled in the art toderive the method and apparatus of the instant invention. In particular,the observed laser oscillation and the relationship between thepulsewidth and the intracavity sample absorptivity represent a newthermooptic phenomenon based on the well-known negative thermal lensformation in laser heated materials.

4. The instant inventors have published a brief abstract which is not anenabling disclosure. In "Measurement of Weak Optical Absorptions byThermally Induced Laser Pulsing," by David A. Cremers and Richard A.Keller, Conference on Lasers and Electro-optics Advance Program,Washington, D.C., June 10-12, 1981 distributed sometime in April, 1981,the authors mention pulsed laser operation when a weakly absorbingsolution is introduced into a misaligned continuous-wave dye lasercavity. However, the key optical component which must be misaligned, andin what manner is not described. For example, a misalignment of theoutput coupler of the dye laser cavity in a horizontal direction whenthe folding mirrors are vertically situated will not produce pulsedoperation, nor will any misalignment of the sample containingintracavity cell.

SUMMARY OF THE INVENTION

An object of the instant invention is to determine the absorptivity ofsamples.

Another object is to determine the absorptivity of solutes in liquid orsolid solution.

Yet another object is to determine the solute concentration in liquidand solid solutions.

Additional objects, advantages and novel features of the invention willbe set forth in part in the description which follows, and in part willbecome apparent to those skilled in the art upon examination of thefollowing or may be learned by practice of the invention. The objectsand advantages of the invention may be realized and attained by means ofthe instrumentalities and combinations particularly pointed out in theappended claims.

To achieve the foregoing and other objects, and in accordance with thepurposes of the present invention, as embodied and broadly describedherein, the apparatus of this invention may comprise a cavity of anormally continuous-wave laser into which a cell containing the sampleunder investigation is inserted and which has its output couplerdeliberately tilted relative to laser light circulating within thecavity such that stable, pulsed laser output is obtained in place ofcontinuous-wave oscillation. Preferably, such laser cavity includes acontinuous-wave laser-pumped dye laser cavity. It is also preferred thatsuch cavity further comprises an end mirror, a beam folding mirror, adye solution jet stream placed in between the beam folding mirror andthe end mirror, an aperture placed in front of the beam folding mirror,and a Lyot filter for selection of the wavelength of the dye lasercavity output. A light transmitting cell containing the solution ormaterial under investigation is inserted into the dye laser cavity inbetween the output coupler and the Lyot filter, and is oriented atapproximately Brewster's angle relative to circulating laser light. Thedye solution jet stream is excited by a continuous-wave pump laserwhich, were it not for the tilted output coupler, would ordinarily causecontinuous-wave-dye laser output. However, the tilt of the outputcoupler causes pulsed laser output, essential to the operation of theinstant invention, the width of the output pulses bearing an inverselinear relationship to the absorptivity of the sample. It is preferredthat the angle of tilt of the output coupler relative to the circulatinglaser light be such that it is the largest angle away from normalincidence that will support stable, pulsed laser operation, and in theplane of the position of the remaining optical components of the cavity.Preferrably also, very high reflectance output couplers are used tofurther improve the stability of the pulsed cavity output by increasingthe circulating intracavity laser radiation. This cavity output isdetected, amplified, averaged and recorded using conventional,commercially available electronics. The pulsewidth determinationderivable therefrom is a measure of the sample absorptivity.

In a further aspect of the present invention, in accordance with itsobjects and purposes, the method hereof may also comprise inserting acell containing a liquid or solid solution of the solute for whichabsorotivity or concentration information is required, or a pure liquidor solid for which a value for the absorptivity is sought into thecavity of a normally continuous-wave output laser, the output coupler ofwhich is deliberately misaligned to induce pulsed laser operation whichconsists of equally-spaced output pulses having identical pulsewidthsresulting from the thermal lensing phenomenon occurring inside thesample cell due to the interaction of the sample with laser radiationcirculating within the cavity, and measuring the pulsewidth which can berelated to the sample absorptivity. An algorithm is used to extract theabsorptivity of a pure liquid or solid from measured pulsewidths andvalues of the average intracavity circulating laser power. To obtainsolute concentration or absorptivity information, calibration curves ofpulsewidth versus concentration of the solute in a solution using thesame solvent as the unknown solution, or pulsewidth versus absorptivityfor a solution of a solute of known absorptivity in the same solvent asthe solution under investigation, respectively, both with the sourcecell pathlength, are first generated. The unknown concentration orabsorptivity is then simply read from the appropriate curvecorresponding to the measured pulsewidth of the solution underinvestigation. It is preferred that this cavity includes a laser-pumped,continuous-wave dye laser cavity. It is also preferred that the outputcoupler be tilted relative to the direction of the circulatingintracavity laser radiation at the maximum angle that will sustainstable pulsed operation of the dye laser, and in the plane of the otherlaser cavity components.

In summary, then, the apparatus and method of the present inventionexploits the thermal lensing phenomenon to convert a continuous-waveoperation laser-pumped dye laser to pulsed output when a sample cellcontaining a substance to be investigated is inserted into the dye lasercavity, and the output coupler is deliberately misaligned relative tointracavity circulating laser light. The pulsewidth of this output is ameasure of the absorptivity of the sample and can be used to determinethis quantity and for evaluating the concentration of a solute insolution. Advantages of the instant invention are (1) modest equipmentrequirements; (2) simple measurements with no critical laser alignments;(3) good reproducibility; and (4) high sensitivity.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and form a part ofthe specification, illustrate an embodiment of the present inventionand, together with the description, serve to explain the principles ofthe invention. In the drawings:

FIG. 1 is a schematic representation of the dye laser showing the tiltof the output coupler from the optimum continuous-wave operation opticalpath.

FIG. 2 is an oscilloscope trace of the detected dye laser output for anintracavity inserted sample of pure methanol.

FIG. 3 is a schematic representation of the entire apparatus used tomeasure the pulsewidths and circulating intracavity laser power obtainedfrom the pulsed dye laser operation.

FIG. 4 is a graph of the measured pulsewidth, Δt, versus soluteabsorptivity, α_(s), for solutions of iodine in carbon tetrachloride,the different plotting symbols referring to measurements made on one ofthree days.

FIG. 5 shows the variation of the measured pulsewidth, Δt, with pumplaser power for an intracavity sample of pure methanol; the optimumoperating point being at higher pump laser powers.

FIG. 6 is a graph of the measured pulsewidth, Δt, scaled by the averagecirculating laser power, P_(c), as a function of solute absorptivity,α_(s), for the dye crystal violet dissolved in methanol.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

If a cell containing a weakly absorbing solution is subjected to laserradiation, changes occur in the illuminating beam as it passes throughthe cell. Such changes are a manifestation of the thermooptic effect,and are related to the heating of the liquid in the region traversed bythe laser beam. Generally, if the absorbed laser power is sufficientlysmall, a simple negative thermal lens which defocuses the laser beam isformed in the liquid. This lens results from very small variations inrefractive index of the liquid across the beam due to the heating. If acell containing a sample to be investigated is positioned at Brewster'sangle in the cavity of a normally continuous-wave operation laser-pumpeddye laser for which the output coupler is tilted slightly off-axisrelative to intracavity circulating laser light, the dye laser goes intoa pulsed mode of operation. If the output coupler is not tilted, thepresence of a solution having finite absorption in the cell causes ablooming of the continuous wave laser output, or may even extinguish thelaser oscillation. The laser output in the above-mentioned pulsed modeof operation, consists of a series of equally-spaced pulses havingidentical pulsewidths. The pulse frequency, which generally lies between3 and 10 Hz for all solutions investigated, is relatively independent ofsample absorptivity. Similarly, it is only slightly dependent upon thecavity alignment. The pulsewidth, on the other hand, is stronglydependent upon the absorptivity of the sample, and may decrease by asmuch as a factor of 100 as the absorptivity is increased. Thisphenomenon has been used to measure an absorptivity of less than 10⁻⁵cm⁻¹, while other techniques based on the thermooptic affect have beenused to determine absorptivities in the range 10⁻³ -10⁻⁵ cm⁻¹.

Reference will now be made in detail to the present preferred embodimentof the invention, an example of which is illustrated in the accompanyingdrawings.

FIG. 1 shows the components of the normally continuous-wave laser-pumpedjet stream dye laser cavity, which is the basis of the apparatus of theinstant invention. A sample cell 2 is inserted in between an outputcoupler 1 and a Lyot filter 3. For small cells, the entire cell can beoriented in such a manner that parallel laser radiation transmittingwindows between which the sample under investigation is located aresituated at approximately Brewster's angle relative to intracavitycirculating laser radiation. Longer cells, necessary for measurement ofextremely small absorptivities, are oriented with the body of the cellalong the intracavity circulating laser radiation, while the lasertransmitting end windows, between which the sample lies, areindividually located at Brewster's angle, to minimize reflective lossesto the intracavity laser radiation which necessarily traverses the cell.A folding mirror 4 and an end mirror 5 complete the optical componentsnecessary for laser operation, and surround the continuous-wavelaser-pumped jet stream 6 which is schematically indicated as flowinginto the plane of the figure. The pumping laser radiation 9 is shown toenter parallel to the plane of the figure. In normal operation, thecirculating laser radiation inside the dye laser cavity 7 impinges uponthe output coupler 1 in normal incidence. However, the apparatus andmethod of the instant invention requires a slight tilt of the outputcoupler in the vertical direction which shifts the beam along the pathdesignated schematically by the broken line 8. This induces theaforementioned pulsed operation output. It was found that a horizontaltilt of the output coupler will not result in the desired pulsed output.Preferably, the dye laser cavity is pumped with about 5.2 W of 515 nmradiation from an argon ion laser. For those experiments requiring a 10cm path length cell with Brewster angle windows, the output couplermirror was mounted externally to the cavity to permit insertion of thelonger cell into the cavity, while for short cells, those withpathlength of the order of 1.29 cm, cell insertion could achievedwithout cavity modification. Stability of pulsed operation was enhancedby increasing the circulating intracavity laser power through the use ofhigh reflectance output couplers. Reflectances of the output coupler atthe two wavelengths used in the reduction to practice of our inventionwere 0.9989 (583 nm) and 0.9993 (633 nm). Wavelength selection wasachieved by a Lyot filter 3, and preferably, the lasing dye solution wasrhodamine 6 G in ethylene glycol at a concentration of about 1.5 g/l. Itshould be mentioned at this point that it would be obvious to oneskilled in the appropriate art that the instant invention would beoperable using any normally continuous-wave operation laser. A dye laserwas chosen so that more than one wavelength could be investigated.

FIG. 2 shows the dye laser output when operating in the pulsed modewhere the output coupler has been deliberately misaligned and a sampleof pure methanol has been inserted intracavity. It is seen that theoutput is a series of equally-spaced pulses having identicalpulsewidths. For a fixed tilt of the output coupler, the frequency ofpulsed operation is relatively constant for solutions of different totalabsorptivity, those with different solvents, and for changes in cavityalignment. In the majority of cases, the pulsing frequency was between3-10 Hz, although the frequency could be controlled to a limited extentwithin 1-15 Hz by adjustment of the angle of tilt of the output coupler.It was found, that as the angle of tilt is reduced, the pulsingfrequency increases until continuous-wave lasing is achieved.Preferably, the mirror is given the maximum angle of tilt that wouldsustain pulsed operation. This corresponds to about 0.9 milliradiansvertically (either up or down) as measured from the mirror position atwhich optimum continuous-wave operation occurs. The pulsewidth, on theother hand, is strongly dependent upon the absorptivity of the samplesolution and may decrease by as much as a factor of 100 as the sampleabsorptivity is increased. It is this fact that renders the apparatusand method of the instant invention useful for measuring weakabsorptivities of solutions which can yield solute concentrationinformation, and the absorptivities of solutes in solution and of pureliquids. Reference 1, described hereinabove, reports oscillation oflaser power due to an intracavity thermal lens when the laser wasoperated near threshold. The stability of the oscillations of the methodand apparatus of the instant invention, however, increases as thecirculating laser power is increased.

FIG. 3 shows the entire apparatus used to record and average the pulsedoperation pulsewidths. The above-described dye laser 10 is combined withcommercially available electronics and optical components in order toaccomplish these measurements. Attenuated dye laser output pulses aremonitored by an intensity calibrated photodiode 14. The photodiodesignal is amplified 15 and then averaged by a digital storageoscilloscope 16 and recorded on a hard copy recording device 17. Thesweep of the signal averager was externally triggered by a secondphotodiode 13 positioned to intercept light reflected from the Lyotfilter 3. Generally, 128 separate pulses were averaged to produce asingle pulsewidth measurement. The intracavity circulating laser powerwas measured using the calibrated photodiode 14 to monitor the intensityof radiation transmitted by the output coupler. The power in the cavitywas then calculated from the known transmittance of the mirror.

Solutions containing solutes of known absorptivity were used in many ofthe measurements. At wavelengths of 583 nm and 633 nm, the quantum yieldof conversion of electronic energy into heat is essentially unity forthese solutes so that all of the light absorbed is turned into heateffective in forming the thermal lens. Dilute solutions of each solutewere prepared from more concentrated solutions for which theabsorptivities were measured with a conventional spectrophotometer. FIG.4 shows the results of the pulsewidth measurements made with solutionsof I₂ /CCl₄. The three different symbols depict the results taken overthree separate days, and indicate the day-to-day reproducibility of thelaser pulsing technique, and further, that the pulsewidth is insensitiveto small variations in position of the sample cell in the cavity.Because of the low absorptivity of carbon tetrachloride, it wasnecessary to use a long pathlength cell to obtain steady pulsedoperation. A 10 cm cell of fused pyrex with Brewster angle windows wasemployed for these measurements.

The pulsewidth is related to the total absorptivity of the solution atthe lasing wavelength. The maximum absorptivity that can be measuredwith the method and apparatus of the instant invention is determined bythe intracavity circulating laser power. That is, the loss introduced bythe absorbing solution cannot be large enough to extinguish laseraction. To be noticed in FIG. 4, for the experimental conditions of thepreferred embodiment of the instant invention, lasing could not bemaintained using solutions of iodine/carbon tetrachloride (contained ina 10 cm cell) having absorptivities greater than ˜7×10⁻⁴ cm⁻¹. Forsolutions of crystal violet in methanol (contained in a 1.29 cmpathlength cell), lasing could be achieved for absorptivities of up to˜10⁻² cm⁻¹.

FIG. 5 shows the dependence of the pulsewidth upon pump laser power forpure methanol in the sample cell. Optimal measurement conditionsoccurred when the laser pump power was approximately 5 watts.

Visual inspection of laser light scattered by the solution in the samplecell shows that the vertical dimension of the laser beam increasesduring each pulse. The change in the laser beam is best described as aspreading of the beam either up or down from the position of the beam atthe start of the pulse. The direction in which the beam spreads isdetermined by the tilt of the output coupler mirror. For example, whenthe top of the mirror is tilted inward, the beam spreads upward in thecavity. On the other hand, for an outward tilt of the mirror top, thebeam spreads downward during the pulse. This behavior rules outconvection as a significant factor inducing pulsed operation. In bothcases, the most intense portion of the spreading beam lies along themoving edge of the beam. The maximum spread of the beam in the cavity isabout 1 mm. These visual observations were confirmed by measurements ofthe laser beam profile using a linear photodiode array. Theseobservations suggest the mechanism by which the laser pulsing occurs.Referring again to FIG. 1, the laser axis which results in the highestpower and best mode quality is designated by the solid line 7. A newlasing axis, resulting from the tilt of the output mirror 1, isdesignated by the dashed line 8. As the angle between these two lines isincreased, the output power of the laser decreases, until an angle isreached where lasing ceases. This angle can be controlled by theaperture 11 placed in front of folding mirror 4. With the insertion of asample cell into the cavity which has been deliberately misaligned andinitially lases along the axis designated by the dashed line 8, heatingbegins in the sample and the beam spreads upward, with the most intensepart approaching the solid line 7 until lasing ceases. This process isrepeated during every pulse. The movement of the beam may be explainedby noting that the formation of an off-axis, negative thermal lens inthe cavity can compensate for misalignment of the planar output coupler.This can be demonstrated mathematically. The variation of cavity gainwith the angle between the solid and the dashed lines also has a role inpulsed laser operation. At the start of each pulse, lasing occurs alongthe dashed line as described hereinabove, and the negative thermal lensformed initially will have this dashed line as its axis. The lens thenproduces rays which diverge from this axis both above and below. Thoserays closer to the solid line experience greater gain than the raysfurther away. Because of this, a new thermal lens is formed around thoserays in between the dashed and solid lines. There is therefore atraveling thermal lens like element in the sample which follows theupward (or downward) motion of the laser beam. It is necessary to tiltthe output coupler mirror to produce pulsed operation because only inthis configuration can the thermal lens like element formed in thesample correct for the misaligned cavity. In contrast, the formation ofa thermal lens in a perfectly aligned cavity produces rays divergingfrom the solid line characterized by a reduced gain. The regenerativeaspect of laser amplification does not reinforce any of these divergentrays in the aligned configuration, whereas, for the case of a tiltedoutput coupler, rays that are closest to the solid line arepreferentially amplified. The most likely processes responsible forswitching the laser oscillation off, thereby producing pulsed output,may include loss of sufficient gain to sustain lasing because ofspreading of the laser beam during a pulse, and the merging of thethermal lens axis with the solid line so that the lens can no longersimultaneously correct for cavity misalignment and permit lasing near oralong the solid axis.

Although the thermal lens acts to produce lasing along the solid axis,where the gain is greatest, a steady-state cannot be attained along anyaxis in the presence of a thermal lens in the misaligned cavity. Thereason for this, which also can be shown theoretically, is that in thesteady state, the axis of the laser beam and the thermal lens must becoincident, and in this case the corrective power of the thermal lens iszero. For this reason, the steady state is unstable and the laser canonly operate in the dynamic situation in which the axis of the thermallens lags behind the axis of the most intense part of the laser beam. Ifa permanent lens were to be placed in the laser cavity to correct forthe misalignment of the output coupler, continuous laser operation couldbe made to occur. However, the thermal lens disappears in the regionbehind the moving laser beam because of conductive cooling of the sampleso that the corrective process cannot be permanently maintained.

To illustrate the apparatus and method of the instant invention, thefollowing examples are presented. First, however, a description ispresented of how the measurements performed can be used to measure theabsorptivity of samples, and to determine the concentration of a solutein solution. FIG. 6 shows a plot of P_(c) Δt versus solute absorptivity(α_(s)) for solutions of crystal violet in methanol (absorptivity ofmethanol is approximately 10⁻³ cm⁻¹), where P_(c) is the intracavitycirculating laser power at full-width at one-half-maximum of the outputpulse. To be noticed is that P_(c) Δt approaches a constant value atboth large and small values of α_(s). For small α_(s), the nearconstancy of P_(c) Δt is an indication that α_(s) is much less than α₀,where α₀ is the solvent absorptivity, so a small change in α_(s) willnot significantly change the overall absorptivity of the sample. Forlarge α_(s), the near constancy of the ordinate is most likely to resultfrom the change in the mechanism responsible for turning off the laser.As the first example, the absorptivity of a pure solvent, methanol, iscalculated from the data which comprises FIG. 6. The basic algorithm forperforming such calculations is:

    (P.sub.c Δt)×(α.sub.0 +α.sub.s)=q,

where q is a constant. This equation can be written in a more convenientform:

    (P.sub.c Δt).sup.-1 =α.sub.s /q+α.sub.0 /q=mα.sub.s +b,                                                       (1)

where α_(s), α₀, Δt, and P_(c) have all been previously defined. Using asimple linear regression calculation and the known values of α_(s), themeasured values of P_(c) Δt can be fit to Eq. (1) to determine m and b.The ratio b/m is computed to find α₀. The precision of α₀ is ##EQU1##and σ_(b) and σ_(m) are the standard deviations of the quantities b andm, respectively. The values of b, m, and α₀ obtained for water,methanol, acetone, and carbon tetrachloride are listed in Table 1 alongwith the standard deviations (σ_(b), σ_(m)) and the correlationcoefficient (r²). Published absorptivity values of these solvents at theappropriate wavelengths are also listed in this table.

The value obtained for water absorption at 583 nm using the apparatusand method of the instant invention and Eq.(1) is in good agreement withthe published values. The precision of our measurement is 17%, whichshows absorptivities of pure solvents can be determined accurately. Theabsorptivity of methanol reported in Table 1 is about five times greaterthan that obtained by workers using a dual beam thermal lensingapparatus. However, they suggest that their number is most likelyunreliable, and should be scaled upward. See, e.g., M. S. Burberry, J.A. Morrel, A. C. Albrecht, and R. L. Swofford, J. Chem. Phys, 70, 552(1979), which is hereby incorporated by reference. No value for theabsorptivity of acetone is reported at 583 nm in the previousliterature. The apparatus and method of this invention therefore caneasily be used to determine accurately the absorption of a pure solvent.However, for solutions with absorptivities greater than approximately10⁻², there is difficulty in maintaining the pulsed laser operation socritical to the instant invention. This effectively establishes an upperlimit to the utility of the invention. To establish an estimate of thelower detection limit for the laser pulsing technique, the absorptivityof CCl₄ at 633 nm was determined. A steady, pulsed laser output couldnot be achieved with pure carbon tetrachloride in the 1.29 cm pathlengthcell used for the other measurements reported. However, stable pulsingwas obtained with CCl₄ in a 10 cm cell. Table I shows the absorptivityof CCl₄ to be (3.95±3.62)×10⁻⁶ cm⁻¹. The only previously reported valuewas that the absorptivity of CCl₄ was less than 10⁻⁵ cm⁻¹, which ourvalue certainly satisfies. The low precision of our measurement islikely an indication that the weak absorption of carbon tetrachloride ismarginally adequate to sustain pulsed operation even in a 10 cm cell atthe reduced circulating power levels in the cavity at 633 nm compared tomuch higher values thereof at 583 nm. However, the data was veryreproducible over a period of three days. In view of these results, areasonable detection limit for our invention would be approximately4×10⁻⁶ cm⁻¹ for a 10 cm cell and the other conditions quoted.

                                      TABLE I                                     __________________________________________________________________________    Measured Absorptivities.                                                             wavelength                     10.sup.4 · α.sub.o                                                     10.sup.4 ·                                                           α.sub.o (published)       solvent                                                                              (nm)  m ± σ.sub.m                                                                    b ± σ.sub.b                                                                      r.sup.2a                                                                         (cm.sup.-1)                                                                           (cm.sup.-1)                     __________________________________________________________________________    water  583   (2.86 ± 0.12) × 10.sup.4                                                       (3.56 ± 0.46) × 10.sup.1                                                         0.985                                                                            12.4 ± 2.1                                                                         (10.8-14.0).sup.b               CH.sub.3 OH                                                                          583   (3.58 ± 0.03) × 10.sup.3                                                       (3.60 ± 0.26)                                                                          0.999                                                                            10.1 ± 0.8                                                                         2.sup.c                         CH.sub.3 COCH.sub.3                                                                  583   (1.14 ± 0.03) × 10.sup.5                                                       (1.98 ± 0.09) × 10.sup.1                                                         0.996                                                                            1.74 ± 0.12                                                                        --                              CCl.sub.4                                                                            633   (5.04 ± 0.28) × 10.sup.2                                                         (1.99 ± 1.71) × 10.sup.-3                                                      0.960                                                                            0.0395 ± 0.0362                                                                    <0.1.sup.d                      __________________________________________________________________________     .sup.a Correlation coefficient = r.sup.2.                                     .sup.b R. C. Smith and K. S. Baker, Appl. Opt. 20, 177 (1981).                 .sup.c R. L. Swofford, M. E. Long, M. S. Burberry, and A. C. Albrecht, J     Chem. Phys. 66, 664 (1977).                                                   .sup.d J. Stone, J. Opt. Soc. Am. 62, 327 (1972).                        

The concentration of a solute can be determined using a calibrationcurve of pulsewidth (or P_(c) Δt) versus solute absorptivity (orconcentration) as shown in FIGS. 4 and 6. The solute concentration isthen found by measuring the pulsewidth and P_(c) generated by theunknown solution of interest. Once a calibration curve of Δt versusα_(s) has been prepared for a particular solute in a certain solvent, itcan be used to determine the concentration of other solutes in the samesolvent if the absorptivity and quantum yield for conversion of absorbedlaser light into heat of both the unknown and calibration solutes in thesolvent are known. The absorptivity measured by our invention is theproduct of the true absorptivity times this quantum yield. The reasonfor this is that in the case of weak solutions of a solute, changes insolute concentration only effect the value of the total absorptivity α₀+α_(s) which alters the strength of the thermal lens. The values of theother solution dependent parameters are constant for these weaklyabsorbing solutions and have the value appropriate to the pure solvent.The laser pulsing technique, then, is a sensitive and accurate methodfor determining absorptivities of samples and solute concentrations insolutions.

The ultimate sensitivity of the method is related to the solventemployed. In general, it may not always be possible to realize theminimum detection limit of this invention in measurements of soluteabsorbances because of the interference from large background solventabsorptions. The precision of the data in FIG. 6 indicates that soluteabsorptions of the order of 10% of the total absorptivity can bedistinguished using our invention. That is, an α_(s) of approximately10⁻⁴ cm⁻¹ can be measured in the presence of an α₀ of about 10⁻³ cm⁻¹which is the absorptivity of pure methanol. On the other hand, the dataof FIG. 4 reveals that for iodine/carbon tetrachloride solutions, thesmallest detectable solute absorptivity is on the order of theabsorptivity of pure CCl₄ (3.95×10⁻⁶ cm⁻¹), rather than 10% of thisvalue. The reduction in the ability to resolve solute absorptions is theresult of a decrease in the precision of the data and loss ofsensitivity when measurements are made near the minimum detection limitof this technique. The extension of the apparatus and method of theinstant invention to solutes dissolved in solid solutions isstraightforward.

Advantages of the instant invention are: (1) modest equipmentrequirements; (2) measurements are simple to make with no criticalalignments; (3) good reproducibility of data; and (4) high sensitivity.The best application of the instant technique appears to be thedetermination of solute absorptivities, which can be done rapidly andaccurately, leading to solute concentrations in solution.

The foregoing description of the preferred embodiment of the inventionhas been presented for purposes of illustration and description. It isnot intended to be exhaustive or to limit the invention to the preciseform disclosed, and obviously many modifications and variations arepossible in light of the above teaching. The embodiment was chosen anddescribed in order to best explain the principles of the invention andits practical application to thereby enable others skilled in the art tobest utilize the invention in various embodiments and with variousmodifications as are suited to the particular use contemplated. It isintended that the scope of the invention be defined by the claimsappended hereto.

What is claimed is:
 1. A method for measuring weak solute opticalabsorptivity, α_(s), using the thermal lensing phenomenon, whichcomprises the steps of:a. inserting a cell containing a solution of thesolute in a chosen solvent, into the cavity of a normallycontinuous-wave output laser; b. misaligning the output coupler of saidlaser cavity to induce pulsed laser operation consisting of a series ofequally-spaced output pulses having identical first pulsewidth, whichresult from the thermal lensing phenomenon occurring within said cellbecause of the interaction of said solution with laser radiationcirculating within said cavity; c. measuring said first pulsewidth ofsaid laser output pulse; d. establishing a calibration curve of a seriesof second pulsewidth measurements, Δt, versus solute absorptivity,α_(s), for said chosen solvent and a solute of known absorptivity andhaving unit efficiency for the conversion of absorbed laser light intoheat, placed in said cell in said laser cavity; and e. comparing saidfirst measured pulsewidth with said calibration curve to locate thecorresponding absorptivity which is the desired solute opticalabsorptivity because for weakly absorbing solutions, total absorptivitydepends substantially upon the solute absorptivity and the absorption ofthe solvent and not on the nature of the solute.
 2. A method formeasuring weak solvent optical absorptivity, α_(o), using the thermallensing phenomenon, which comprises the steps of:a. inserting a cellcontaining a solution of a chosen solute of known absorptivity, α_(s),and having unit efficiency for the conversion of absorbed laser lightinto heat in the solvent into the cavity of a normally continuous-waveoutput laser; b. misaligning the output coupler of said laser cavity toinduce pulsed laser operation consisting of a series of equally-spacedoutput pulses having identical first pulsewidth, Δt, which result fromthe thermal lensing phenomenon occurring in said cell because of theinteraction of said solution with laser radiation circulating withinsaid cavity; c. measuring said first pulsewidth of said laser outputpulses; d. measuring a first intracavity circulating laser power, P_(c),at the full-width-at-one-half-maximum point of said pulsed laser outputfor said first solute absorptivity; e. changing said known absorptivity,α_(s), of said chosen solute in the solvent in said cell and determininganother pulsewidth and another intracavity circulating laser powerresulting from a change in total absorptivity, α_(o) +α_(s) ; f.repeating said changing of said known absorptivity of said chosen solutein the solvent in said cell step and said determining of laserpulsewidth and said intracavity circulating laser power to obtain aplurality of said laser pulsewidth and said intracavity laser powermeasurements; and g. relating said pulsewidth and said intracavity laserpower measurements and said known solute absorptivity to the solventabsorptivity according to the formula (α_(o) +α_(s)) P_(c) Δt=constant,from which α₀ and said constant can be extracted by mathematicalcurve-fitting.
 3. A method for measuring unknown solute concentration inweakly absorbing solid or liquid solutions using the thermal lensingphenomenon, which comprises the steps of:a. inserting a cell containingthe solution into the cavity of a normally continuous-wave output laser;b. misaligning the output coupler of said laser cavity to induce pulsedlaser operation consisting of a series of equally-spaced output pulseshaving identical first pulsewidth, which result from the thermal lensingphenomenon occurring within said cell because of the interaction of saidsolution with laser radiation circulating within said cavity; c.measuring said first pulsewidth of said laser output pulse; d.establishing a calibration curve of a series of second pulsewidthmeasurements, Δt, versus solute concentration using the same solvent andsolute as exist in the unknown solution; and e. comparing said firstmeasured pulsewidth with said calibration curve to locate thecorresponding solute concentration which is the desired unknown soluteconcentration.
 4. A method for measuring solute molar extinctioncoefficients, ε_(s), using the thermal lensing phenomenon, for solutionsof known solute concentration, c, and where the quantum yield forconversion of absorbed laser light into heat for the solute, Φ, isknown, which comprises the steps of:a. inserting a cell containing asolution of the solute in a chosen solvent into the cavity of a normallycontinuous-wave output laser; b. misaligning the output coupler of saidlaser cavity to induce pulsed laser operation consisting of a series ofequally-spaced output pulses having identical first pulsewidth, whichresult from the thermal lensing phenomenon occurring within said cellbecause of the interaction of said solution with laser radiationcirculating within said cavity; c. measuring and recording said firstpulsewidth of said laser output pulse; d. establishing a calibrationcurve of a series of second pulsewidth measurements, Δt, versus soluteabsorptivity, α_(s), for said chosen solvent and a solute of knownabsorptivity and having unit efficiency for the conversion of absorbedlaser light into heat placed in said laser cavity; e. comparing saidfirst measured pulsewidth with said calibration curve to locate thecorresponding measured absorptivity which is the measured opticalabsorptivity of the solute of interest because for weakly absorbingsolutions, total absorptivity depends substantially upon the soluteabsorptivity and the absorption of the solvent and not on the nature ofthe solute; and f. extracting the molar extinction coefficient, ε_(s),from the relationship ε_(s) =α_(m) /Φc, where α_(m) is said measuredoptical absorptivity of the solute of interest obtained from saidcalibration curve.
 5. The method as described in claims 1, 2, 3, or 4,wherein said laser cavity includes a continuous-wave laser-pumped dyelaser cavity.
 6. The method as described in claim 5, wherein said lasercavity output coupler misaligning step gives said output coupler themaximum angle of tilt relative to the direction of said circulatinglaser radiation that will sustain said pulsed laser operation.
 7. Anapparatus for measuring weak optical absorptivity of pure samples, andof solutes in liquid and solid solution, the concentration of a solutein liquid and solid solutions, and the molar extinction coefficient of asolute in liquid and solid solutions, which comprises in combination:a.a normally continuous-wave output laser, the cavity of which furthercomprises:i. an output coupler which is tilted relative to laserradiation circulating within said cavity such that stable pulsed laseroutput is obtained in place of normally continuous-wave output, thepulsewidth of which is related to the total absorptivity of the materialunder investigation; and ii. a light-transmitting cell through whichsaid circulating intracavity laser radiation passes and which containsthe material under investigation; b. means for quantitatively detectingsaid laser pulsewidth and the average intracavity circulating laserpower P_(c) ; and c. means for recording output from said detectingmeans.
 8. The apparatus as described in claim 7, wherein said normallycontinuous-wave output laser includes a laser-pumped, normallycontinuous-wave output dye laser, which further comprises:i. an outputcoupler which is tilted relative to laser radiation circulating withinsaid cavity such that stable pulsed dye laser output is obtained inplace of normally continuous-wave output; ii. a beam folding mirror;iii. an end mirror; approximately Brewster's angle relative to saidcirculating laser light; and vii. a continuous-wave pump laser to excitesaid dye solution.
 9. The apparatus as described in claim 8, whereinsaid dye solution is introduced into said dye laser in a continuous jetstream.
 10. The apparatus as described in claim 9, wherein saidwavelength selection means includes a Lyot filter.
 11. The apparatus asdescribed in claim 10, wherein an aperture is placed in front of saidbeam folding mirror to control the mode structure of said intracavitycirculating laser radiation.
 12. The apparatus as described in claim 11,wherein said output coupler has a reflectance in excess of about 0.99 inorder to enhance the stability of said pulsed output by increasing thecirculating laser power within said laser cavity.
 13. The apparatus asdescribed in claim 12, wherein said pump laser includes an argon-ionlaser operating at about 515 nm and producing approximately 5 W ofpower.
 14. The apparatus of claim 13, wherein said dye solution includesrhodamine 6G in ethylene glycol at a concentration of about 1.5 g/l. 15.The apparatus as described in claims 7 or 14, wherein said tilted outputcoupler is given the maximum angle of tilt that will sustain said pulsedoutput operation of said laser cavity.